Question

Construct a rectangle having a diagonal of 7cm and length of one of its sides is 4 cm. Find its area also.

Answer 1

Hint: Whenever you are asked to construct a rectangle it is advised to construct a rough diagram which will help in finding a suitable answer.

Complete step-by-step answer:
Given, Diagonal=7 cm and length of one side =4 cm. Steps for construction:
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB =4 cm.
Step 3 : Construct BX \[ \bot \]AB 
Step 4 : With A as center, draw an arc of radius 7 cm which cuts BX at C.
Step 5 : With BC as radius, draw an arc above AB with A as center.
Step 6 : With C as center, and 4 cm radius, draw an arc to cut the previous arc at D.
Step 7 : Join AD and CD. ABCD is the required rectangle.
Step 8: Measure the length of BC. BC=l=5.8 cm

Note: Whenever you construct a rectangle, the 2 sides will always equal. For example, AB=DC=4cm the same way AD=BC. Whenever a diagonal is constructed to a rectangle, it forms a triangle which helps in finding the area of the rectangle.